3 research outputs found
Quantum Phases of Cold Polar Molecules in 2D Optical Lattices
We discuss the quantum phases of hard-core bosons on a two-dimensional square
lattice interacting via repulsive dipole-dipole interactions, as realizable
with polar molecules trapped in optical lattices. In the limit of small
tunneling, we find evidence for a devil's staircase, where solid phases appear
at all rational fillings of the underlying lattice. For finite tunneling, we
establish the existence of extended regions of parameters where the groundstate
is a supersolid, obtained by doping the solids either with particles or
vacancies. Here the solid-superfluid quantum melting transition consists of two
consecutive second-order transitions, with a supersolid as the intermediate
phase. The effects of finite temperature and confining potentials relevant to
experiments are discussed.Comment: replaced with published versio
The physics of dipolar bosonic quantum gases
This article reviews the recent theoretical and experimental advances in the
study of ultracold gases made of bosonic particles interacting via the
long-range, anisotropic dipole-dipole interaction, in addition to the
short-range and isotropic contact interaction usually at work in ultracold
gases. The specific properties emerging from the dipolar interaction are
emphasized, from the mean-field regime valid for dilute Bose-Einstein
condensates, to the strongly correlated regimes reached for dipolar bosons in
optical lattices.Comment: Review article, 71 pages, 35 figures, 350 references. Submitted to
Reports on Progress in Physic
Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
Topological color codes are among the stabilizer codes with remarkable
properties from quantum information perspective. In this paper we construct a
four-valent lattice, the so called ruby lattice, governed by a 2-body
Hamiltonian. In a particular regime of coupling constants, degenerate
perturbation theory implies that the low energy spectrum of the model can be
described by a many-body effective Hamiltonian, which encodes the color code as
its ground state subspace. The gauge symmetry
of color code could already be realized by
identifying three distinct plaquette operators on the lattice. Plaquettes are
extended to closed strings or string-net structures. Non-contractible closed
strings winding the space commute with Hamiltonian but not always with each
other giving rise to exact topological degeneracy of the model. Connection to
2-colexes can be established at the non-perturbative level. The particular
structure of the 2-body Hamiltonian provides a fruitful interpretation in terms
of mapping to bosons coupled to effective spins. We show that high energy
excitations of the model have fermionic statistics. They form three families of
high energy excitations each of one color. Furthermore, we show that they
belong to a particular family of topological charges. Also, we use
Jordan-Wigner transformation in order to test the integrability of the model
via introducing of Majorana fermions. The four-valent structure of the lattice
prevents to reduce the fermionized Hamiltonian into a quadratic form due to
interacting gauge fields. We also propose another construction for 2-body
Hamiltonian based on the connection between color codes and cluster states. We
discuss this latter approach along the construction based on the ruby lattice.Comment: 56 pages, 16 figures, published version